A swelling seal sleeve is known from e.g. WO03/008756, WO06/003113 and US2007/0056735. In all these publications the seal sleeves disclosed therein are annular objects with a swelling seal sleeve wall with a radial wall thickness in a non-swollen state and an increased radial wall thickness in a swollen state. In general, these swelling seal sleeves may be mounted on an inner element having an outer surface that has to be introduced into an outer element having an inner surface. The inner element may, for example, be production tubing that has to be introduced into a bore well hole. In that example, the bore well hole or the casing thereof is the outer element.